Quiz 2: Inverse Trigonometric Functions

https://cdn.lti.glynlyon.com/media/07e914b4-1ded-44f3-b133-16e33b06f543/img/graph_arctanx.gif

Click on the graph below to choose the graph of the function y = arctan(x).

- π/4 sec π = 1/cos π = 1/(-1) = -1 The range of arctangent is - π/2 to π/2, and the angle whose tangent is 1 is π/4. arctan(sec π) = arctan(-1) = -π/4

Evaluate arctan(secπ).

15/17 The range of arctangent is -90° to 90°, so arctan(-8/15) results in a fourth-quadrant angle. Tangent is opposite over adjacent.Find the hypotenuse: 8² + 15² = c² c = 17 Since the angle is a fourth-quadrant angle, the cosine is positive. Cosine is adjacent over hypotenuse: 15/17.

Evaluate cos[arctan(-8/15)].

4

Find the number of solutions for the given equation for 0° ≤ θ ≤ 360°. sec²θ = 2

8 1/4 cot x - 11 = -9 1/4 cot x = 2 cot x = 8

If 1/4 cotx - 11 = -9, then cotx = _____.

300, 180, 60

Select all the solutions of the given equation for 0° < θ < 360°. secθsinθ - 2sinθ = 0

undefined 2 is not in the domain of arccosine.

Simplify arccos2.

60°

Simplify arccot √3/3

π/3 The angle whose secant is 2 has a cosine of 1/2.

Simplify arcsec2.

-60° 240° is not in the range of arcsine, so find a coterminal angle that is.

Simplify arcsin(sin240°).

undefined 1/2 is not in the domain of arcsecant.

Simplify sec(arcsec1/2).

{77°} https://assets.learnosity.com/organisations/328/ea9e9c34-818c-4d34-a124-ac58e2c9b6b8/soln_2cossqx_plus4cosx_minus1.gif Use a calculator in degree mode: 2 +/- + 6 INV x² = ÷ 2 = INV cos This gives 77.0°. The other solution is not in the domain of arccosine.

Solve 2cos²x + 4cosx - 1 = 0 for 0° ≤ x < 180°.

5π/6, 11π/6

Solve 3tanx + √3 = 0 for 0 ≤ x < 2π.

168.5° csc ²θ - cscθ - 20 = 0 (cscθ - 5)(cscθ + 4) = 0 cscθ = 5 or cscθ = -4 (sinθ = 1/5 or sinθ = -1/4) Use a calculator in degree mode: 5 1/x INV sin This gives 11.5°. Sine is also positive in Quadrant II: 180 - 11.5 = 168.5° Use a calculator in degree mode: 4 +/- 1/x INV sin This gives -14.5°, or 360 - 14.5 = 345.5°. Sine is also negative in Quadrant III:180 + 14.5 = 194.5°

Which of the following angles is in the solution set of csc²θ - cscθ - 20 = 0 for 0° ≤ θ < 360°.

-1 ≤ x ≤ 1 all reals x ≤ -1 or x ≥ 1 0° ≤ y ≤ 180° -90° < y < 90°

domain of arcsinx domain of arccotx domain of arccscx range of arccosx range of arctanx